To multiply \( 8 \) by \( 5 \frac{9}{16} \), we first convert the mixed number \( 5 \frac{9}{16} \) into an improper fraction.
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Multiply the whole number by the denominator: \[ 5 \times 16 = 80 \]
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Add the result to the numerator: \[ 80 + 9 = 89 \]
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Therefore, \( 5 \frac{9}{16} \) can be written as: \[ \frac{89}{16} \]
Now, we can multiply \( 8 \) by \( \frac{89}{16} \):
\[ 8 \times \frac{89}{16} = \frac{8 \times 89}{16} = \frac{712}{16} \]
Next, we simplify \( \frac{712}{16} \). We can divide both the numerator and denominator by their greatest common divisor, which is \( 8 \):
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Divide the numerator: \[ 712 \div 8 = 89 \]
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Divide the denominator: \[ 16 \div 8 = 2 \]
Thus, \[ \frac{712}{16} = \frac{89}{2} \]
Finally, we can convert \( \frac{89}{2} \) back to a mixed number:
- Divide \( 89 \) by \( 2 \): \[ 89 \div 2 = 44 \quad \text{(whole number)} \] with a remainder of \( 1 \).
So, \( 89 \div 2 \) gives us: \[ 44 \frac{1}{2} \]
Therefore, the final answer is: \[ 8 \times 5 \frac{9}{16} = 44 \frac{1}{2} \]